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The role of Dr Klemperer, a major character in Luca Guadagnino's remake of the Seventies horror film, was credited to an unheard of actor called "Lutz Ebersdorf", an 82-year-old retired psychoanalyst with no previous film credits.

Given the presence in the film of Swinton, a chameleonic actress who has played everyone from David Bowie to elderly dowagers on screen, many guessed that the British star was lurking beneath the wrinkles. But both director and actress roundly dismissed the notion. Or, as Swinton now admits: never asked the right question in the first place.

“Curiously, to date, nobody has thought of it,” Swinton told the New York Times over email. That question was: “Are you playing Lutz Ebersdorf?” To which Swinton would have answered “an unequivocal yes”. Swinton also appears in the film – more recognisably – as dance instructor Madame Blanc.

There were, Swinton and Guadagnino explained, several grand creative theories behind the disguised casting, in part to do with the themes of psychoanalysis and femininity that run throughout Suspiria, and the fact that Ebersdorf's character was grieving for his late wife. But also, Swinton admitted, it was just a novel thing to do: “for the sheer sake of fun above all,” Swinton wrote. “As my grandmother would have it – a motto to live and die by – ‘Dull Not To.’”

Part of the reason why people remained so baffled by Swinton's disguise was her (and Guadagnino's) commitment to it. He dismissed any notions of subterfuge as “fake news”, and Ebersdorf's absence at Venice was explained by a statement supposedly from him, read by Swinton, which explained that he was “a private person”.

Swinton spent four hours a day having prosthetics and make-up applied to turn her into Ebersdorf. She reunited with Mark Coulier, the Oscar-winning makeup artist who transformed her into an old lady for The Grand Budapest Hotel.

Swinton had specific instructions for Coulier and his team to help her get into character: “She did have us make a penis and balls,” he said.

“She had this nice, weighty set of genitalia so that she could feel it dangling between her legs, and she managed to get it out on set on a couple of occasions.” He added that Swinton didn't keep her bonus prosthetics, which were “probably in a box somewhere!”

Once transformed into Ebersdorf, Swinton tried her best to keep up the ruse, insisting that she was called "Lutz" on set to the extent that some crew members believed they were two separate people. She also made sure that Ebersdorf had an online presence, uploading a headshot to the Internet Movie Databse and writing the fictional man a biography for his web listing.

Had a German paparazzo not submitted photographs of Ebersdorf captioned as Swinton to an agency two years ago (causing Guadignino to believe there was a German mole on the set), she may have been able to achieve her “long-held dream”: “that Lutz would die during the edit, and his ‘In Memoriam’ be the final credit in the film.”